Variable neighborhood search for extremal graphs. 17. further conjectures and results about the index

Mustapha Aouchiche, Hansen Pierre, Dragan Stevanović

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

abs The AutoGraphiX 2 system is used to compare the index of a connected graph G with a number of other graph theoretical invariants, i.e., chromatic number, maximum, minimum and average degree, diameter, radius, average distance, independence and domination numbers. In each case, best possible lower and upper bounds, in terms of the order of G, are sought for sums, di erences, ratios and products of the index and another invariant. There are 72 cases altogether:in 7 cases known results were reproduced, in 32 cases immediate results were obtained and automatically proved by the system, conjectures were obtained in 27 cases, of which 12 were proved (in 3 theorems and 9 propositions), 9 remain open and 6 were refuted. No results could be derived in 7 cases.

Original languageEnglish
Pages (from-to)15-37
Number of pages23
JournalDiscussiones Mathematicae - Graph Theory
Volume29
Issue number1
DOIs
Publication statusPublished - 2009
Externally publishedYes

Keywords

  • AutoGraphiX
  • Automated conjecture making
  • Graph invariant
  • Index of a graph
  • Spectral radius

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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